Spatial Shortcuts in Graph Neural Controlled Differential Equations

Michael Detzel, Gabriel Nobis, Jackie Ma, Wojciech Samek

Keywords: neural controlled differential equations, advection simulation, time series forecasting, causal modeling, prior knowledge, inductive bias, graphs

TL;DR: We inform a Neural Controlled Differential Equation with graph topology information and train it on simulated advection data

Abstract: We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of simulated advection data on graph edges with a known causal graph, observed only at vertices during training. We investigate different positions in the model architecture to inform the NCDE with graph information and identify an outer position between hidden state and control as theoretically and empirically favorable. Our such informed NCDE requires fewer parameters to reach a lower Mean Absolute Error (MAE) compared to previous methods that do not incorporate additional graph topology information.

Submission Number: 35